Define $f : \mathbb { R } \rightarrow \mathbb { R }$ by
$$f ( x ) = \begin{cases} ( 1 - \cos x ) \sin \left( \frac { 1 } { x } \right) , & x \neq 0 \\ 0 , & x = 0 \end{cases}$$
Then,\\
(A) $f$ is discontinuous.\\
(B) $f$ is continuous but not differentiable.\\
(C) $f$ is differentiable and its derivative is discontinuous.\\
(D) $f$ is differentiable and its derivative is continuous.